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Dynamics Kinetics (1) A 2000-kg car is stopped from an initial speed of 100 kph in a distance of 75 m. Assuming that all four wheels contribute equally to the braking force, determine the braking force F at each wheel knowing that the car has a constant deceleration. 50 kg (2) The 50-kg crate is resting on a 15-degree P inclined plane. The coefficient of static friction is 150 0.20 and coefficient of kinetic friction is 0.15 at the surface of contact between the crate and the plane. If a force P, acting upward and parallel to the inclined plane is applied to the crate, determine the resulting acceleration of the crate if (a) P=0, (b) P=150N, and (c) P= 300N. 100kg (3) The system is released from rest with the cable taut. The coefficients of frictions are  s = 0.25 and k = 0.20 , calculate the acceleration of each body and the tension T in the cable. Neglect the mass and friction of the pulleys. (4) Determine the accelerations of bodies A and B and the tension in the cable due to the application of the 250-N force. Neglect al friction and the masses in the pulleys.

40kg

300

680N

340N

B

A

(5) A 0.5-kg block slides on a circular path of radius 4 m in a vertical plane. It is known that the speed of the block is 4 m/s as it passes the lowest point A and 3 m/s as it passes point B. Determine the force exerted on the block by the surface at points A and B.

P=250N

250 v

4m B

(6) Find the angle of banking for a highway curve of 100 m radius design to accommodate cars travelling at 160 kph, if the coefficient of friction between the tires and the road is 0.60. What is the rated speed of the curve?

A

(7) A weight of 450 N is attached to a rope which is wrapped around a 1-m diameter solid cylinder weighing 1400 N. The cylinder rotates about its horizontal axis. Compute the angular acceleration of the cylinder and the tension in the rope. (8) A block weighing 432 N is dropped from a height 1.2 m upon a spring whose modulus is 18 N/mm. What velocity will the spring have at the instant the spring is deformed 100 mm? Ans close to 4.66 m/s (9) A golf ball is dropped from a height of 20 ft upon a hardened steel plate. The coefficient of restitution is 0.894. Find the height to which the ball rebounds on the first, second, and third bounces. (10) A ball is thrown with velocity of 50 ft per sec directed 600 with the horizontal against a smooth vertical wall. The ball is released from a position 40 ft from the wall and 6 ft above the level ground and travels in the vertical plane. The coefficient of restitution between the ball and the wall is 0.6. How far does the ball strike the ground? (Ans 18.3 ft) (11) A projectile is launched from point A and has a horizontal range L1 as shown. B A If the coefficient of restitution is at B is e, determine the distance L2. (ans L2=eL1) L1 L2 (12) A child throws a ball from point A with a speed of 15 m/s. It strikes a vertical wall located 3 m horizontally away from A and the ball returns exactly at point A. Determine the necessary angle of release of the ball with respect to the horizontal if the coefficient of restitution in the wall impact is 0.5. (Ans close to 11.37 or 78.6) (13) The simple 2-kg pendulum is released from rest in the horizontal position. As it reaches 800mm he bottom position, the cord wraps around the smooth fixed pin at B and continues in the 400mm smaller arc in the vertical plane. Calculate the B magnitude of the force R supported by the pin at 0 B when the pendulum passes the position  = 30 θ .